Theorem bianass 469

Description: An inference to merge two lists of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019.)

Hypothesis

Ref	Expression
bianass.1	|- ( ph <-> ( ps /\ ch ) )

Assertion

Ref	Expression
bianass	|- ( ( et /\ ph ) <-> ( ( et /\ ps ) /\ ch ) )

Proof of Theorem bianass

Step	Hyp	Ref	Expression
1		bianass.1	. . 3 |- ( ph <-> ( ps /\ ch ) )
2	1	anbi2i 457	. 2 |- ( ( et /\ ph ) <-> ( et /\ ( ps /\ ch ) ) )
3		anass 401	. 2 |- ( ( ( et /\ ps ) /\ ch ) <-> ( et /\ ( ps /\ ch ) ) )
4	2, 3	bitr4i 187	1 |- ( ( et /\ ph ) <-> ( ( et /\ ps ) /\ ch ) )

Syntax hints:   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  bianassc  470